Answer:
Let's assume that the colors on the cube are numbered as follows:
Red
Blue
Green
Yellow
Purple
Orange
Without loss of generality, we can assume that the face numbered 1 is painted red. We can then use the following table to determine the colors of the other faces:
Face Number Color Opposite Face Number Opposite Color
1 Red 6 Orange
2 Blue 5 Purple
3 Green 4 Yellow
4 Yellow 3 Green
5 Purple 2 Blue
6 Orange 1 Red
We can start by choosing the color for face number 2, which must be one of the colors opposite to red (i.e., purple, green, or yellow). Let's say we choose purple. Then, the color for face number 5 must be one of the colors opposite to blue (i.e., green or yellow). Let's say we choose green. Then, the color for face number 3 must be one of the colors opposite to yellow (i.e., purple or orange). Let's say we choose orange. Now, the remaining three colors must be the ones that have not been used yet, which are blue, green, and yellow. We can then assign them to faces 4, 6, and 1, respectively.
Therefore, the numbering of the faces is as follows:
Face Number Color
1 Yellow
2 Purple
3 Orange
4 Green
5 Green
6 Blue
Note that we could have started by choosing green for face number 2 instead of purple, which would have led to a different numbering. However, we would have ended up with the same set of six colors.
In general, there are 3 choices for the color of face number 2, 2 choices for the color of face number 5, and 2 choices for the color of face number 3. After those choices are made, there is only one way to assign the remaining three colors to the remaining three faces. Therefore, there are:
3 x 2 x 2 x 1 = 12
different ways to number the faces of the cube as described in the problem.
Step-by-step explanation:
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NEED HELP WILL GIVE BRAINLIEST AND 5 STARS I HAVE 20 MINUTES PLEASE HELP!
For this rational function, find the domain of m(x)
Answer:
hope this helps in some form of a way....im not that good with math:(
Step-by-step explanation:
PLEASE HELP IT MEANS ALOT TYSM
Applying the inscribed angle theorem, the value of x in the given circle is: x = 35.
How to Apply the Inscribed Angle Theorem?In the circle given, angle NWT is an inscribed angle in the given diagram and arc NT is the intercepted arc. According to the inscribed angle we have the following equation which we would use to solve for the value of x:
m<NWT = 1/2(measure of arc NT)
Plug in the values:
54 = 1/2(x + 2x + 3)
2(54) = x + 2x + 3
108 = 3x + 3
Solve for x:
108 - 3 = 3x
105 = 3x
105/3 = x
x = 35
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12 Look at the expression below.
1/2 (a + b) - (a - b)²
What is the value of the expression
when a = 18 and b = 14?
A 32
B
12
C8
D 0
2
Finn cuts a board that is 8 ft long into two pieces, where one piece is 48 inches longer than the other piece. Find the length of each piece
The shorter piece is ________ft long
The longer piece is ________ ft long.
Thank you in advance for your help!
Graph the following linear equation.
Determine the slope and y - intercept
Y=3x +2
Answer air undefined is selected, the slope value is undefined. Otherwise, the box value is used.
A graph of the linear equation is shown below.
The slope of this linear equation is equal to 3.
The y-intercept of this linear equation is equal to 2.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, a linear equation that models the line is represented by this mathematical equation;
y = mx + c
y = 3x + 2
By comparison, we have the following:
mx = 3x
Slope, m = 3.
Initial value or y-intercept, c = 2.
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Isabel is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $121 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
The range of mileages that Company A would charge less than Company B would be m > 80.
How to find the mileages ?The function for Company A is $ 121 to show that the company price does not change.
The function of Company B would be 65 + 0. 70 m to show that $ 0.70 is charged per mile.
The mileage where Company B charges more is:
121 < 65 + 0. 70 m
56 < 0. 70 m
m > 56 / 0. 70
m > 80
In conclusion, when the miles are over 80 miles, then Company B is more expensive.
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Model Question 1) J Ina Surve among 330 Students. It was found that Viso liked Mathematics, Looliked Social and 50 likes both subjects. Then find the number of students who. i) like at least one Subject. Like at most one Subject w did not like mathematics and Science iv) like only one Subjeet v illustrate the above information in Venn diagram
the number of students who like at least one subject cannot be determined from the given information. The number of students who like at most one subject and did not like Mathematics and Science is s, and the number of students who like only one subject is m + s - 100.
How to solve the question?
Based on the given information, we can construct a Venn diagram with three sets: M (Mathematics), S (Social), and N (None or neither Mathematics nor Social). Let the number of students who like Mathematics, Social, and neither be denoted by m, s, and n, respectively.
We know that there are 330 students in total, and 50 of them like both Mathematics and Social. Thus, we can start filling in the diagram as follows:
Next, we know that m + 50 students like Mathematics, and s + 50 students like Social. However, we have to subtract the 50 students who like both from both groups to avoid double-counting. Therefore:
m + 50 - 50 = m
s + 50 - 50 = s
We also know that there are no students who like neither Mathematics nor Social, so n = 0.
Now, we can use the principle of inclusion-exclusion to find the number of students who like at least one subject. This is simply the union of the three sets M, S, and N:
| M ∪ S ∪ N | = | M | + | S | + | N | - | M ∩ S | - | M ∩ N | - | S ∩ N | + | M ∩ S ∩ N |
| M ∪ S ∪ N | = m + s + 0 - 50 - 0 - 0 + 50
| M ∪ S ∪ N | = m + s
Therefore, the number of students who like at least one subject is m + s, which we can't determine from the given information.
To find the number of students who like at most one subject and did not like Mathematics and Science, we need to focus on the sets S and N. Since we know that n = 0, we can simplify the diagram:
We are looking for the number of students who like at most one subject and did not like Mathematics and Science, which is simply the set S (since no one likes neither Mathematics nor Social). Therefore, the number of students who like at most one subject and did not like Mathematics and Science is s.
Finally, to find the number of students who like only one subject, we need to subtract the number of students who like both subjects from the total number of students who like at least one subject:
| M ∪ S | = | M | + | S | - | M ∩ S |
| M ∪ S | = m + s - 50
The number of students who like only one subject is therefore:
| M ∪ S | - | M ∩ S | = (m + s - 50) - 50 = m + s - 100
In summary, the number of students who like at least one subject cannot be determined from the given information. The number of students who like at most one subject and did not like Mathematics and Science is s, and the number of students who like only one subject is m + s - 100.
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(c) Figure 6 shows the triangle ABC, with all side lengths measured in centimetres.
side AB = 14.6 cm
side AC = 21.4 cm
side BC = 7.5 cm
(i) Find angle ABC, giving your answer correct to the nearest degree.
(ii) Find the area of triangle ABC, giving your answer correct to the nearest square centimetre.
Answer:
angle B ≈ 149°area ≈ 28 cm²Step-by-step explanation:
You want the largest angle and the area of a triangle with side lengths 7.5 cm, 14.6 cm, and 21.4 cm.
Law of cosinesThe law of cosines tells you ...
b² = a² + c² -2ac·cos(B)
Solving for angle B, we have ...
B = arccos((a² +c² -b²)/(2ac))
B = arccos((7.5² +14.6² -21.4²)/(2·7.5·14.6)) ≈ 149° . . . angle ABC
AreaThe area of the triangle can be found using the formula ...
Area = 1/2(ac·sin(B))
Area = 1/2·7.5·14.6·sin(149°) ≈ 28 cm² . . . area
__
Additional comment
Angle ABC is opposite side AC, which is the longest side. Hence, angle ABC is the largest angle.
We used the original (full precision) angle value to calculate the area. The rounded angle value would be inappropriate for that purpose. (Second attachment.) Note the calculator mode is set to DEGrees.
what is 10% of 480kg
3) Calculate the shaded area for the given figure.
←4-
The shaded area for the given figure is equal to 10.32 square units.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length or height of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = 4 × 12
Area of rectangle = 48 square units.
For the total area of circle, we have:
Area of circle, A = πr²
Total area of circle, T = 3 × 3.14 × (4/2)²
Total area of circle, T = 37.68 square units.
Shaded area = 48 square units - 37.68 square units.
Shaded area = 10.32 square units
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Use the graphing tool to graph the equation of the cosine function . Then determine the amplitude and the period of the function.1/2
A graph of the equation of the cosine function is shown below.
The amplitude of the cosine function is equal to 1/2.
The period of the cosine function is equal to 8π.
How to graph and determine the amplitude and period of a function?In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).Based on the information about this cosine function, it is denoted by;
f(x) = 1/2cos(1/4x) - 1
By comparison, we have the following:
Amplitude, A = 1/2.
B = 1/4
1/4 = 2π/P
Period, P = 2π × 4 = 8π
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The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown.
A graph titled Grabbing Pretzels has handspan (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20).
Predictor Coef SE Coef t-ratio p
Constant -14.71 4.317 1.689 0.046
Handspan 1.585 0.310 5.114 0.000
S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7%
Using the computer output, what is the predicted number of pretzels a person with a handspan of 21 cm could grab?
a) 8.10 pretzels
b) 10.83 pretzels
c) 18.58 pretzels
d) 75.95 pretzels
The slope of the Least-Square Regression Line is 1.585 from the regression output given, hence, for each additional increase in hand span, the number of pretzels increases by 1.585
Given that,
A graph titled Grabbing Pretzels has hand span (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20).
Predictor Coef SE Coef t-ratio p
Constant -14.71 4.317 1.689 0.046
Hand spun 1.585 0.310 5.114 0.000
S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7%
The slope of a linear regression line gives the rate of increase in y-value per change in x
The Handspun Coefficient on the table is the slope of the regression line
Therefore, for every 1 centimeter increase in handspun, number of pretzels increases by 1.585
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complete question:
The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown.
A graph titled Grabbing Pretzels has handspan (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20).
Predictor Coef SE Coef t-ratio p
Constant -14.71 4.317 1.689 0.046
Handspan 1.585 0.310 5.114 0.000
S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7%
Using the computer output, the slope of the least-squares regression line means for each additional
In △EFG
, m∠E=(8x+5)°
, m∠F=(x−11)°
, and m∠G=(2x−1)°
. What is m∠E
to the nearest degree?
Answer: 141 °
Step-by-step explanation:
we know sum of angles of a triangle is always 180°.(Angle sum property)
then,
∠E+∠F+∠G=180°
8x+5+2x-1+x-11=180°
11x-7=180C
x=187/11
x=17°
m∠E=8x+15=8*17+5=141°
Thabang is a cyclist on an avareage of 500 in 1 minute determine the formula for distance
The required formula for distance is distance = 500t, where t is the time in minutes and distance is the distance traveled in the corresponding time.
If Thabang's speed is 500 units per minute, then the formula for distance traveled in a certain amount of time t in minutes would be:
distance = speed x time
In this case, Tha bang's speed is 500 units per minute, so the formula becomes:
distance = 500t
Where t is the time in minutes and distance is the distance traveled in the corresponding time.
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7
A number cube was rolled as part of an experiment. The results are displayed in the table below.
Number
Frequency
1 2
3
4 6 5
4
7
5 6
3 ¹5
What is the best explanation of how to find the experimental probability of rolling a 3?
O To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total
number of trials. Simplify if necessary.
O To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the
number three. Simplify if necessary.
O To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials.
Simplify if necessary.
To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three.
Simplify if necessary.
Answer:
To find the experimental probability of rolling a 3, we need to write a ratio of the number of times 3 occurs to the total number of trials. Therefore, the best explanation of how to find the experimental probability of rolling a 3 is:
Step-by-step explanation:
"To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary."
In this case, we can see from the table that the number 3 occurs 5 times out of a total of 35 trials. Therefore, the experimental probability of rolling a 3 is:
experimental probability of rolling a 3 = number of times 3 occurs / total number of trials
experimental probability of rolling a 3 = 5 / 35
experimental probability of rolling a 3 = 1/7
Therefore, the experimental probability of rolling a 3 is 1/7, or approximately 0.143 or 14.3%.
3The number of boys in a mixed school is 280. The ratio of boys to girls is 4: 5. Find the total number of students in the school.
Answer:
124
Step-by-step explanation:
add 4 and 5 which gives you 9
the solve 280 x 4/9
and you get 124
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The statistics guru on the board of directors was right! Too many of the orders will be free with the new promotion Connie was so excited to launch. Suppose the board likes the idea of the promotion but wants Connie to adjust the time so that only about 5% of the orders will be free. If 5% of the orders are free, 95% are ready within the goal time frame. Use this information to determine what the new goal time for the promotion should be. Type the correct answer in each box. Use numerals instead of words. Express the time in minutes and seconds, to the nearest second. The time used for the promotion should be minutes, seconds.
The new goal time for the promotion should be 3 minutes and 42 seconds in order to ensure that only about 5% of the orders will be free.
We can use the inverse of the cumulative distribution function of a normal distribution with a mean of the goal time and a standard deviation of 2 minutes and 15 seconds to find the new goal time.
Specifically, we want to find the time t such that the area under the normal distribution curve to the left of t is 0.95 (since we want 95% of orders to be within the goal time frame).
Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.95 to the left is approximately 1.645.
We know that the standard normal distribution has a mean of 0 and a standard deviation of 1, so we can set up the following equation:
1.645 = (t - goal time) / (2 minutes + 15 seconds expressed in decimal minutes)
Solving for t, we get:
t = goal time + 1.645 * (2.25 minutes)
Since we want the answer in minutes and seconds, we can convert the decimal minutes back to minutes and seconds:
2.25 minutes = 2 minutes + 0.25 minutes
= 2 minutes + 0.25 * 60 seconds
= 2 minutes + 15 seconds
Substituting this back into the equation for t, we get:
t = goal time + 1.645 * (2 minutes + 15 seconds)
= goal time + 3.70725
To solve for the new goal time, we need to round to the nearest second:
t ≈ goal time + 3.707 ≈ goal time + 3.71
Since we want about 5% of orders to be free, the goal time should be set at 3 minutes and 42 seconds.
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Natalie is planning a field day for all the third and fourth graders.
There are 35 students in each of the 3 third grade classrooms and a
total of 112 fourth graders. She wants to have 6 groups and divide
the students as evenly as possible. How can she arrange the
students in groups so that they are as even as possible?
Answer:
5 groups of 36 with one group with 37.
Hope this helps!
Step-by-step explanation:
35 students × 3 classes = 105 total number of third graders
105 third graders + 112 fourth graders = 217 total number of students
217 students ÷ 6 groups = 36.16666... students in each group
Because students cannot be decimals or fractions and have to be whole, there will be 5 groups of 36 with a 6th group with 37 students.
36 + 36 + 36 + 36 + 36 + 37 = 217
Eren asked Levi, "In general, how tall are giraffes?"
Is this a statistical question?
Answer:
Yes
Step-by-step explanation:
This is a statistical question because you have to collect statistical data to answer the question
José is at an antique car show. He records
the types of cars he sees in the table. What
is the experimental probability for each type
of car he sees at the car show?
The experimental probability for each type of car that José sees at the car show is determined using the formula:
Probability of each car = number of each car seen/total number of cars What is experimental probability?Experimental probability is one that is primarily based on a series of tests.
A random experiment is carried out and repeatedly repeated, with each repetition acting as a trial, to assess their likelihood.
Because the goal of the experiment is to ascertain the likelihood that an event will occur, or whether it will occur at all.
Examples include tossing a coin, rolling dice, or spinning a spinner. In mathematics, the probability of an event is always equal to its frequency divided by the total number of trials.
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The angle, in degrees, at which a batter hits a baseball can affect the distance the ball
travels, in feet. The function B(x) = -0.2x² + 14x - 21 models the distance the baseball
travels in ft. depending on the angle, in degrees, at which the ball is hit.
What does the Variable x represent? Include the units.
What does the variable y represent? Include the units.
Interpret the y-intercept. Include units.
The variable x represents the angle at which the baseball is hit in degrees.
The variable y represents the baseball's distance traveled in feet.
The y-intercept of the function B(x) reflects the distance traveled by the baseball when it is struck at a 0 degree angle, i.e. directly horizontally.
How to explain the functionThe distance traveled in this situation is given by:
B(0) = -0.2(0)² + 14(0) - 21 = -21
As a result, the y-intercept is -21 feet, indicating that if the baseball is hit horizontally, it will travel 21 feet backwards. However, because a baseball cannot be hit horizontally, the y-intercept is not a useful value.
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Calculator What is the volume of this sphere? 8m cm³
Step-by-step explanation:
the formula
4/3πr3
so
36π cm3 is the answer
Answer: 113.1 cm³
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^{3}[/tex] r=3
= [tex]\frac{4}{3} \pi 3^{3}[/tex]
[tex]=36\pi[/tex]
=113.1 cm³
Find the length of the hypotenuse. Round your answer to the nearest tenth if necessary.
Answer:
a^2 + b^2 = c^2
8^2 + 15^2 = c^2
64 + 225 = c^2
289 = c^2
17 = c
The hypotenuse is 17.
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NO LINKS!!! URGENT HELP PLEASE!!!!
How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years? Round your answer to the nearest cent
A = 300,000
r = 3.6
t = 14
I NEED HELP FAST!!!
A cone has a radius of 2 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 6 inches?
Enter your answer in the box.
Surface area of similar cone =
in²
What are the coordinates of the image of the point (-9,4) after a 90 degree clockwise rotation followed by a translation 3 units right?
The coordinates of the rotated image is P' ( 7 , 9 )
To find the image of the point (-9, 4) after a 90 degree clockwise rotation followed by a translation 3 units right
Rotate the point (-9, 4) 90° clockwise
(x', y') = (y, -x)
On simplifying , we get
(x1, y1) = (4, -(-9)) = (4, 9)
Translate the point 3 units right:
To translate a point to the right, we add the translation distance to the x-coordinate
So, applying this translation, we get:
(x2, y2) = (4+3, 9) = (7, 9)
Hence , the coordinates of the image of the point (-9, 4) after a 90 degree clockwise rotation followed by a translation 3 units right are (7, 9)
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-8 times 8 - [-4+4-(-3)]=
Answer:
-67
Step-by-step explanation:
-8 · 8 - [-4+4-(-3)]
= -64 - [-4+4-(-3)]
= -64 - [-4+4+3]
= -64 - [3]
= -64 - 3
= -67
2^2 x 2^3 as a positive single exponet
The expression with a single positive exponent is:
[tex]2^5[/tex]
How to rewrite the expression with a single exponent?Remember the rule for a product of two powers with the same base:
[tex]x^n*x^m = x^{n + m}[/tex]
So we just need to add the two exponents (remember that we only can do this when the two bases are the same ones)
In this case, we have the expression:
[tex]2^2*2^3[/tex]
In both powers the base is 2, then we can just use the rule defined above and add the exponents, we will get the expression:
[tex]2^2*2^3 = 2^{2 + 3} = 2^5[/tex]
That is the expression with a single positive exponent.
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A large random sample of female German Shepherd dogs found that the height of the dogs had a normal distribution with a mean height of 23.2 inches and a standard deviation of 0.8 inches. Based on this, what percent of female German Shepherds would be more than 22.7 inches tall?
Answer:
73.4%
Step-by-step explanation:
The standardized value, or z-score, for a height of 22.7 inches can be calculated as:
z = (22.7 - 23.2) / 0.8 = -0.625
Using a standard normal distribution table, we can find that the area to the right of z = -0.625 is 0.734, or 73.4%.
Which ordered pair best describes the point plotted in Quadrant I on the coordinate plane shown?
(4, -6)
(4, 6)
(6, 4)
(-4, 6)
Answer:
(4, 6)
Step-by-step explanation:
The first quadrant is in the top right, second is in bottom right, third in bottom left, and fourth in top left.
The x-axis is told by the first number listed in the point (#, #), and the y-axis is listed in the second number.
(4, -6) is in the second quadrant and is listed on the graph.
(4, 6) is in the first quadrant and is listed on the graph.
(6, 4) is in the first quadrant and is not listed on the graph.
(-4, 6) is in the fourth quadrant and is not listed on the graph.
(the point in the third quadrant is at the point (-4, -6), which is not listed)
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